Euler's line

In geometry, Euler's line (red line in the image) is the line passing through the orthocenter (blue), the circumcenter (green), the centroid (yellow), and the center of the nine point circle (red point) of any triangle.

Leonhard Euler showed that in any triangle, those four points are collinear. The center of the nine point circle lies midway between the orthocenter and the circumcenter, and the distance from the centroid to the circumcenter is half that from the centroid to the orthocenter.

External Links

• Altitudes and the Euler Line
• Euler Line and 9-Point Circle